Commuting homogeneous locally nilpotent derivations

Abstract

Abstract Let be an affine algebraic variety endowed with an action of complexity one of an algebraic torus . It is well known that homogeneous locally nilpotent derivations on the algebra of regular functions can be described in terms of proper polyhedral divisors corresponding to the -variety . We prove that homogeneous locally nilpotent derivations commute if and only if a certain combinatorial criterion holds. These results are used to describe actions of unipotent groups of dimension two on affine -varieties. Bibliography: 10 titles.